A six sigma event is an observation that falls six standard deviations away from the average, sigma being the usual symbol for standard deviation. Under a normal distribution, the probability of a move at least that large in one direction is about one in a billion. For a daily return, that corresponds to roughly one occurrence in four million years of trading.
Markets produce such moves far more often than the normal curve allows. The fall in United States share prices on 19 October 1987 was more than twenty standard deviations by the measures of the time. The gap reflects fat tails and changing volatility and is a standard criticism of risk models such as value at risk that assume normality. The phrase is related to the idea of a black swan event and is unrelated to the Six Sigma method of quality management.